H1: the route, class, and release criteria

The distinction in item (iii) does not prohibit a future generalized operator theorem. It requires that theorem to be stated and proved rather than supplied by terminology.

The endings concern only the internal relations and common operator representation:

1. Constructed: the necessary internal relation and amplitude maps exist, and one common representation is justified on a stated domain.

2. Proved obstructed: a demonstrated incompatibility excludes every representation in Definition def:class.

3. Unresolved: an internal amplitude map, matching hypothesis, or common representation remains missing.

A constructed representation would not by itself discharge the joint-section, remainder, or quantum-admission gates.